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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(labrd, "Laborde") "\n\tCyl, Sph\n\tSpecial for Madagascar";
#define EPS 1.e-10
struct pj_opaque {
double kRg, p0s, A, C, Ca, Cb, Cc, Cd; \
int rot;
};
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double V1, V2, ps, sinps, cosps, sinps2, cosps2;
double I1, I2, I3, I4, I5, I6, x2, y2, t;
V1 = Q->A * log( tan(M_FORTPI + .5 * lp.phi) );
t = P->e * sin(lp.phi);
V2 = .5 * P->e * Q->A * log ((1. + t)/(1. - t));
ps = 2. * (atan(exp(V1 - V2 + Q->C)) - M_FORTPI);
I1 = ps - Q->p0s;
cosps = cos(ps); cosps2 = cosps * cosps;
sinps = sin(ps); sinps2 = sinps * sinps;
I4 = Q->A * cosps;
I2 = .5 * Q->A * I4 * sinps;
I3 = I2 * Q->A * Q->A * (5. * cosps2 - sinps2) / 12.;
I6 = I4 * Q->A * Q->A;
I5 = I6 * (cosps2 - sinps2) / 6.;
I6 *= Q->A * Q->A *
(5. * cosps2 * cosps2 + sinps2 * (sinps2 - 18. * cosps2)) / 120.;
t = lp.lam * lp.lam;
xy.x = Q->kRg * lp.lam * (I4 + t * (I5 + t * I6));
xy.y = Q->kRg * (I1 + t * (I2 + t * I3));
x2 = xy.x * xy.x;
y2 = xy.y * xy.y;
V1 = 3. * xy.x * y2 - xy.x * x2;
V2 = xy.y * y2 - 3. * x2 * xy.y;
xy.x += Q->Ca * V1 + Q->Cb * V2;
xy.y += Q->Ca * V2 - Q->Cb * V1;
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double x2, y2, V1, V2, V3, V4, t, t2, ps, pe, tpe, s;
double I7, I8, I9, I10, I11, d, Re;
int i;
x2 = xy.x * xy.x;
y2 = xy.y * xy.y;
V1 = 3. * xy.x * y2 - xy.x * x2;
V2 = xy.y * y2 - 3. * x2 * xy.y;
V3 = xy.x * (5. * y2 * y2 + x2 * (-10. * y2 + x2 ));
V4 = xy.y * (5. * x2 * x2 + y2 * (-10. * x2 + y2 ));
xy.x += - Q->Ca * V1 - Q->Cb * V2 + Q->Cc * V3 + Q->Cd * V4;
xy.y += Q->Cb * V1 - Q->Ca * V2 - Q->Cd * V3 + Q->Cc * V4;
ps = Q->p0s + xy.y / Q->kRg;
pe = ps + P->phi0 - Q->p0s;
for ( i = 20; i; --i) {
V1 = Q->A * log(tan(M_FORTPI + .5 * pe));
tpe = P->e * sin(pe);
V2 = .5 * P->e * Q->A * log((1. + tpe)/(1. - tpe));
t = ps - 2. * (atan(exp(V1 - V2 + Q->C)) - M_FORTPI);
pe += t;
if (fabs(t) < EPS)
break;
}
t = P->e * sin(pe);
t = 1. - t * t;
Re = P->one_es / ( t * sqrt(t) );
t = tan(ps);
t2 = t * t;
s = Q->kRg * Q->kRg;
d = Re * P->k0 * Q->kRg;
I7 = t / (2. * d);
I8 = t * (5. + 3. * t2) / (24. * d * s);
d = cos(ps) * Q->kRg * Q->A;
I9 = 1. / d;
d *= s;
I10 = (1. + 2. * t2) / (6. * d);
I11 = (5. + t2 * (28. + 24. * t2)) / (120. * d * s);
x2 = xy.x * xy.x;
lp.phi = pe + x2 * (-I7 + I8 * x2);
lp.lam = xy.x * (I9 + x2 * (-I10 + x2 * I11));
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_dealloc (P);
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(labrd) {
double Az, sinp, R, N, t;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
Q->rot = pj_param(P->ctx, P->params, "bno_rot").i == 0;
Az = pj_param(P->ctx, P->params, "razi").f;
sinp = sin(P->phi0);
t = 1. - P->es * sinp * sinp;
N = 1. / sqrt(t);
R = P->one_es * N / t;
Q->kRg = P->k0 * sqrt( N * R );
Q->p0s = atan( sqrt(R / N) * tan(P->phi0) );
Q->A = sinp / sin(Q->p0s);
t = P->e * sinp;
Q->C = .5 * P->e * Q->A * log((1. + t)/(1. - t)) +
- Q->A * log( tan(M_FORTPI + .5 * P->phi0))
+ log( tan(M_FORTPI + .5 * Q->p0s));
t = Az + Az;
Q->Ca = (1. - cos(t)) * ( Q->Cb = 1. / (12. * Q->kRg * Q->kRg) );
Q->Cb *= sin(t);
Q->Cc = 3. * (Q->Ca * Q->Ca - Q->Cb * Q->Cb);
Q->Cd = 6. * Q->Ca * Q->Cb;
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_labrd_selftest (void) {return 0;}
#else
int pj_labrd_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=labrd +ellps=GRS80 +lon_0=0.5 +lat_0=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 166973.166090228391, -110536.912730266107},
{ 166973.168287157256, -331761.993650884193},
{-278345.500519976194, -110469.032642031714},
{-278345.504185269645, -331829.870790275279},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{0.501797719349373672, 2.00090435742047923},
{0.501797717380853658, 1.99909564058898681},
{0.498202280650626328, 2.00090435742047923},
{0.498202282619146342, 1.99909564058898681},
};
return pj_generic_selftest (e_args, 0, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, 0, inv_in, e_inv_expect, 0);
}
#endif
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